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CODE DESIGN BASED ON METRIC-SPECTRUM. Edition No. 1

VDM Publishing House, Sep 2008, Pages: 192


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We introduced nested search methods to design (n,k)
block codes for arbitrary channels by optimizing an
appropriate metric spectrum in each iteration. For a
given k, the methods start with a good high rate
code, say k/(k + 1), and successively design lower
rate codes up to rate k/2^k corresponding to a
Hadamard code. The design methodology was extended
to the generic complex codes by utilizing columns of
newly derived or existing unitary codes. Extensive
comparisons to metric bounds and to previously
designed codes show the optimality or near-
optimality of the new codes. Further, the method was
generalized such that good codes for arbitrary
channels can be designed given the corresponding
metric or the pairwise error probability. Finally,
the introduction of the asymptotically optimum
convolutional codes for a given constraint length,
reduces dramatically the search size for good
convolutional codes of a certain asymptotic
performance, and the consequences to coded code-
division multiple access (CDMA) system design are
highlighted.



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